Problem: Convert the following equation from slope intercept form to standard form. In other words, if the equation is rewritten to look like $Ax + By = C$, what are the values of $A$, $B$, and $C$ ? Assume $A$ is positive. $y = 3x-3$
Solution: Move the $x$ term to the same side as the $y$ term. $-3x + y = -3$ Multiply both sides by $-1$ so that $A$ will be positive $3x - y = 3$ Inspecting the equation in standard form, we see the following. $\begin{align*}A &= 3\\ B &= -1\\ C &= 3\end{align*}$ Behold! The magic of math, that both equations could represent the same line! $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$